## What is a Function Notation

### What does "Function Notation" mean?

The function notation is a simple and efficient way to write functions, making them easy to write, understand, and evaluate. It uses algebraic expressions to summarize how a function affects the input value to get the desired output value. The relationship between the input and output values is shown by the function $$f(x)$$, read as "$$f$$ of $$x$$".

### How do you evaluate the values of a function notation?

When evaluating function notations for a specific input value, substitute the input value into the algebraic expression that defines the function. When figuring out the value of a function notation, the focus is on one input and the output that goes with it.

Look at the function shown above. When evaluating $$f(x) \ = \ 2x \ + \ 7$$ at $$x \ = \ 9$$, substitute the given input value to evaluate and find the value of $$f(9)$$.
$$f(x) \ = \ 2(9) \ + \ 7 \ = \ 18 \ + \ 7 \ = \ 25$$

### Exercises for Function Notation

1) $$p(s) = 4s \ + \ 2$$, find $$p(8)$$$$\ \Rightarrow \$$

2) $$f(x) = 6x^2 \ + \ x \ + \ 2$$, find $$f(2)$$$$\ \Rightarrow \$$

3) $$f(x) = 11x^2 \ - \ x \ + \ 2$$, find $$f(4)$$$$\ \Rightarrow \$$

4) $$g(t) = 2t^2 \ + \ 3$$, find $$g(9)$$$$\ \Rightarrow \$$

5) $$p(s) = 9s^2 \ + \ 4$$, find $$p(3)$$$$\ \Rightarrow \$$

6) $$m(u) = 10u^2 \ + \ 2$$, find $$m(6)$$$$\ \Rightarrow \$$

7) $$p(s) = 4s^2 \ - \ s \ + \ 9$$, find $$p(9)$$$$\ \Rightarrow \$$

8) $$g(t) = 7t^2 \ + \ t \ + \ 7$$, find $$g(6)$$$$\ \Rightarrow \$$

9) $$m(u) = 5u \ + \ 3$$, find $$m(2)$$$$\ \Rightarrow \$$

10) $$f(x) = 6x \ + \ 7$$, find $$f(8)$$$$\ \Rightarrow \$$

1) $$p(s) = 4s \ + \ 2$$, find $$p(8)$$$$\ \Rightarrow \ \color{red}{p(8) = 34}$$
Solution
Substitute $$8$$ for (s) and solve it:   $$p(8) = 4(8) + 2 = 4 \times 8 + 2 = 32 + 2 = 34$$
2) $$f(x) = 6x^2 \ + \ x \ + \ 2$$, find $$f(2)$$$$\ \Rightarrow \ \color{red}{f(2) = 28}$$
Solution
Substitute \2\ for (x) and solve it:   $$f(2) = 6 \times 2 ^2 + 2 + 2 = 28$$
3) $$f(x) = 11x^2 \ - \ x \ + \ 2$$, find $$f(4)$$$$\ \Rightarrow \ \color{red}{f(4) = 174}$$
Solution
Substitute \4\ for (x) and solve it:   $$f(4) = 11 \times 4 ^2 - 4 + 2 = 174$$
4) $$g(t) = 2t^2 \ + \ 3$$, find $$g(9)$$$$\ \Rightarrow \ \color{red}{g(9) = 165}$$
5) $$p(s) = 9s^2 \ + \ 4$$, find $$p(3)$$$$\ \Rightarrow \ \color{red}{p(3) = 85}$$
6) $$m(u) = 10u^2 \ + \ 2$$, find $$m(6)$$$$\ \Rightarrow \ \color{red}{m(6) = 362}$$
7) $$p(s) = 4s^2 \ - \ s \ + \ 9$$, find $$p(9)$$$$\ \Rightarrow \ \color{red}{p(9) = 324}$$
8) $$g(t) = 7t^2 \ + \ t \ + \ 7$$, find $$g(6)$$$$\ \Rightarrow \ \color{red}{g(6) = 265}$$
9) $$m(u) = 5u \ + \ 3$$, find $$m(2)$$$$\ \Rightarrow \ \color{red}{m(2) = 13}$$
10) $$f(x) = 6x \ + \ 7$$, find $$f(8)$$$$\ \Rightarrow \ \color{red}{f(8) = 55}$$

## Function Notation Practice Quiz

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